• Journal of the Chungcheong Mathematical Society
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• v.26 no.3
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• pp.657-669
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• 2013

A general class of two-point optimal fourth-order methods is proposed for locating multiple roots of a nonlinear equation. We investigate convergence analysis and computational properties for the family. Special and simple cases are considered for real-life applications. Numerical experiments strongly verify the convergence behavior and the developed theory.

• Journal of the Chungcheong Mathematical Society
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• v.29 no.4
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• pp.663-676
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• 2016

In this paper we propose a new family of eighth order optimal methods for solving nonlinear equations by using weight function methods. The methods of the family require three function and one derivative evaluations per step and has order of convergence eight, and so they are optimal in the sense of Kung-Traub hypothesis. Precise analysis of convergence is given. Some members of the family are compared with several existing methods to show their performance and as a result to confirm that our methods are as competitive as compared to them.

• Communications of the Korean Mathematical Society
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• v.33 no.2
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• pp.677-693
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• 2018

In this work, we generalize a family of optimal eighth order weighted-Newton methods to Banach spaces and study its local convergence to approximate a locally-unique solution of a system of nonlinear equations. The convergence in this study is shown under hypotheses only on the first derivative. Our analysis avoids the usual Taylor expansions requiring higher order derivatives but uses generalized Lipschitz-type conditions only on the first derivative. Moreover, our new approach provides computable radius of convergence as well as error bounds on the distances involved and estimates on the uniqueness of the solution based on some functions appearing in these generalized conditions. Such estimates are not provided in the approaches using Taylor expansions of higher order derivatives which may not exist or may be very expensive or impossible to compute. The convergence order is computed using computational order of convergence or approximate computational order of convergence which do not require usage of higher derivatives. This technique can be applied to any iterative method using Taylor expansions involving high order derivatives. The study of the local convergence based on Lipschitz constants is important because it provides the degree of difficulty for choosing initial points. In this sense the applicability of the method is expanded. Finally, numerical examples are provided to verify the theoretical results and to show the convergence behavior.

• East Asian mathematical journal
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• v.38 no.3
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• pp.277-292
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• 2022

This study investigates the convergence of the optimal consumption and investment policies in a binomial-tree model to those in the continuous-time model of Merton (1969). We provide the convergence in explicit form and show that the convergence rate is of order ∆t, which is the length of time between consecutive time points. We also show by numerical solutions with realistic parameter values that the optimal policies in the binomial-tree model do not differ significantly from those in the continuous-time model for long-term portfolio management with a horizon over 30 years if rebalancing is done every 6 months.

• Journal of applied mathematics & informatics
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• v.37 no.1_2
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• pp.123-131
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• 2019

In this paper, we introduce a uniform mesh method for a Maxwell's equation with discontinuous coefficients. We observe optimal O(h) order for the electric field and O(h) order for the curl.

• Journal of Ocean Engineering and Technology
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• v.33 no.6
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• pp.607-614
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• 2019

It has been an issue among researchers that the tsunamis that occurred on the west coast of Japan in 1983 and 1993 damaged the coastal cities on the east coast of Korea. In order to predict and reduce the damage to the Korean Peninsula effectively, it is necessary to install offshore tsunami observation instruments as part of the system for the early detection of tsunamis. The purpose of this study is to recommend the optimal deployment of tsunami observation instruments in terms of the higher probability of tsunami detection with the minimum equipment and the maximum evacuation and warning time according to the current situation in Korea. In order to propose the optimal location of the tsunami observation equipment, this study will analyze the tsunami propagation phenomena on the east sea by considering the potential tsunami scenario on the west coast of Japan through numerical modeling using the COrnell Multi-grid COupled Tsunami (COMCOT) model. Based on the results of the numerical model, this study suggested the optimal deployment of Korea's offshore tsunami observation instruments on the northeast side of Ulleung Island.

• Journal of the Korean Mathematical Society
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• v.59 no.6
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• pp.1067-1082
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• 2022

This paper presents a new optimal three-step eighth-order family of iterative methods for finding multiple roots of nonlinear equations. Different from the all existing optimal methods of the eighth-order, the new iterative scheme is constructed using one function and three derivative evaluations per iteration, preserving the efficiency and optimality in the sense of Kung-Traub's conjecture. Theoretical results are verified through several standard numerical test examples. The basins of attraction for several polynomials are also given to illustrate the dynamical behaviour and the obtained results show better stability compared to the recently developed optimal methods.

• Transactions of the Korean Society of Machine Tool Engineers
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• v.12 no.2
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• pp.9-16
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• 2003

A strategy of the optimal shape design with FEA(Finite Element Analysis) for 2-D structure is proposed by comparing subproblem approximation method with first order approximation method. A cantilever beam with two different loading conditions, a concentrated load and an evenly distribute load, and truss structure with a concentrated loading condition are implemented to optimize the shape. It gives a good design strategy on the optimal truss structure as well as the optimal cantilever beam shape. It is found that the convergence is quickly finished with the iteration number below ten. Optimized shapes of cantilever beam and truss structure are shown with stress contour plot by the results of the subproblem approximation method and the first order approximation methd.

• Journal of the Korean Society of Industry Convergence
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• v.20 no.3
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• pp.213-220
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• 2017

This paper proposes an optimal current control method for improving efficiency of Brushless Direct Current (BLDC) motor. The proposed optimal current control method is based on the maximum torque point analysis of Finite Element Analysis (FEA). The proposed method can increase the effective voltage at the maximum torque point of BLDC motor and increase the output torque per unit current to increase the efficiency. In order to verify the proposed optimal current control method, have developed the prototype of a 50 [W] class motor drive and experimented by 20 [W] motor using the dynamometer set. This was verified.

• Bulletin of the Korean Mathematical Society
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• v.44 no.1
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• pp.125-130
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• 2007

We propose a simple and intuitive method to derive the exact convergence rate of global $L_{2}-norm$ error for strong numerical approximation of stochastic differential equations the result of which has been reported by Hofmann and $M{\"u}ller-Gronbach\;(2004)$. We conclude that any strong numerical scheme of order ${\gamma}\;>\;1/2$ has the same optimal convergence rate for this error. The method clearly reveals the structure of global $L_{2}-norm$ error and is similarly applicable for evaluating the convergence rate of global uniform approximations.